Write the fraction you would use to change the base for log8 15 (base 6)
i meant base 8
let x = log8 15
by definition: 8^x = 15
now take log of both sides, (base 10 is understood)
log (8^x) = log 15
x log 8 = log 15
x = log15/log8
in general: loga b = log b/log a , where a ≠ 1, a > 0
To change the base of a logarithm, you can use the logarithm identity formula:
logₐ b = logᵦ b / logᵦ a
In this case, we want to change the base of log₈ 15 from base 6 to some other base. Let's call this new base "c". Therefore, we can rewrite the given logarithm as:
log₈ 15 (base 6) = logᶜ 15 / logᶜ 8
Now we need to identify the base of the logarithm that we want to change to. Since the original base is 6 and we want to change to base "c", we can use the logarithm identity formula to rewrite log₈ 15 as:
log₈ 15 (base 6) = log₆ 15 / log₆ 8 * log₈ 6
Therefore, the fraction we can use to change the base for log₈ 15 (base 6) is log₆ 15 / log₆ 8 * log₈ 6.